P7. What is the future value of $300 deposited into a mutual fund account at the
ID: 2758141 • Letter: P
Question
P7. What is the future value of $300 deposited into a mutual fund account at the end of every month for the next 50 years? Assume that your investment compounds monthly and that you earn 12% per year.
P8. If you buy a house for $300,000 at 3.75% interest, what are your monthly payments for a 30 year conventional loan? If you pay an extra $300 each month, by how much can you reduce the term of your loan?
P9. If you invest $1,000 today and earn $1,000,000 in 40 years, what is your time-compounded annual rate of return?
P10. Suppose that 5 years from now you will receive $10,000 at the end of every year for 5 years. What is the present value of this annuity if the opportunity cost rate is 5%?
Explanation / Answer
P7
FV
= PV * (1+r)^n
n
1 to 600
r
=12%/12 = 1%
Balance at the end of 50 year =
117,475.02
P8
Principal
$300,000
Interest per Annum
3.75%
Interest per month
=3.75%/12
0.31%
n
=30*12
360
EMI
=[Principal*Inerest per month * (1+Interest per Month)^n]/[(1+Interest per month)^n-1]
$ 1,389
If EMI increases by $300 then EMI would be
=$1689
Then Tenure reduces by 100 months
P9
Investment
$1,000
n
40
Target
$1,000,000
r
=[(Target/Investment)^(1/n)]-1
18.9%
P10
n
5
6
7
8
9
FV
10000
10000
10000
10000
10000
r
5%
5%
5%
5%
5%
PV
=10000/(1+5%)^5
=10000/(1+5%)^6
=10000/(1+5%)^7
=10000/(1+5%)^8
=10000/(1+5%)^9
PV
7835.262
7462.154
7106.813
6768.394
6446.089
Sum of PV
35618.71
FV
= PV * (1+r)^n
n
1 to 600
r
=12%/12 = 1%
Balance at the end of 50 year =
117,475.02
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